Package 'andrews' reference manual

Package 'andrews'

Title:	Various Andrews Curves
Description:	Visualisation of multidimensional data through different Andrews curves: Andrews, D. F. (1972) Plots of High-Dimensional Data. Biometrics, 28(1), 125-136. <doi:10.2307/2528964>.
Authors:	Jaroslav Myslivec [aut], Sigbert Klinke [cre, ctb]
Maintainer:	Sigbert Klinke <[email protected]>
License:	GPL-3
Version:	1.1.2
Built:	2025-02-19 04:44:22 UTC
Source:	https://github.com/sigbertklinke/andrews

Title:

Various Andrews Curves

Description:

Visualisation of multidimensional data through different Andrews curves: Andrews, D. F. (1972) Plots of High-Dimensional Data. Biometrics, 28(1), 125-136. <doi:10.2307/2528964>.

Authors:

Jaroslav Myslivec [aut], Sigbert Klinke [cre, ctb]

Maintainer:

Sigbert Klinke <[email protected]>

License:

GPL-3

Version:

1.1.2

Built:

2025-02-19 04:44:22 UTC

Source:

https://github.com/sigbertklinke/andrews

Andrews curves for visualization of multidimensional data. For colouring the curves see the details. For differences between andrews and andrews0 see the vignette("andrews"). With the same parameters called both functions should create the same plot. type==5 is a modification of type==3 and type==6 is a modification of type==4.

Usage

andrews(
  df,
  type = 1,
  clr = NULL,
  step = 100,
  ymax = 10,
  alpha = NULL,
  palcol = NULL,
  lwd = 1,
  lty = "solid",
  ...
)
andrews(
  df,
  type = 1,
  clr = NULL,
  step = 100,
  ymax = 10,
  alpha = NULL,
  palcol = NULL,
  lwd = 1,
  lty = "solid",
  ...
)

Arguments

`df`	data frame or an R object that can be converted into a data frame with `as.data.frame`
`type`	type of curve `1`: $f(t)=x_1/\sqrt{2}+x_2\sin(t)+x_3\cos(t)+x_4\sin(2t)+x_5\cos(2t)+...$ `2`: $f(t)=x_1\sin(t)+x_2\cos(t)+x_3\sin(2t)+x_4\cos(2t)+...$ `3`: $f(t)=x_1\cos(t)+x_2\cos(\sqrt{2t})+x_3\cos(\sqrt{3t})+...$ `4`: $f(t)=0.5^{p/2}x_1+0.5^{(p-1)/2} x_2(\sin(t)+\cos(t))+0.5^{(p-2)/2} x_3(\sin(t)-\cos(t))+0.5^{(p-3)/2} x_4(\sin(2t)+\cos(2t))+0.5^{(p-4)/2}x_5(\sin(2t)-\cos(2t))+...)$ with $p$ the number of variables `5`: $f(t)=x_1\cos(\sqrt{p_0} t)+x_2\cos(\sqrt{p_1}t)+x_3\cos(\sqrt{p_2}t)+...$ with $p_0=1$ and $p_i$ the i-th prime number `6`: $f(t)=1/\sqrt{2}(x_1+x_2(\sin(t)+\cos(t))+x_3(\sin(t)-\cos(t))+x_4(\sin(2t)+\cos(2t))+x_5(\sin(2t)-\cos(2t))+...)$
`clr`	number/name of column in the data frame for color of curves
`step`	smoothness of curves
`ymax`	maximum of `y` coordinate
`alpha`	semi-transparent color ( $0 < alpha < 1$ ) which are supported only on some devices
`palcol`	a function which generates a set of colors, see details
`lwd`	line width, a positive number, defaulting to 1.
`lty`	line type, can either be specified as an integer (0=blank, 1=solid (default), 2=dashed, 3=dotted, 4=dotdash, 5=longdash, 6=twodash) or as one of the character strings "blank", "solid", "dashed", "dotted", "dotdash", "longdash", or "twodash", where "blank" uses ‘invisible lines’ (i.e., does not draw them).
`...`	further named parameters given to `graphics::plot.default()` except `x`, `y`, and `type`.

Details

If clr has length one then it is used as column number or column name for coloring the curves:

If df[,clr] is numeric then palcol must be function which returns colors for values in the range ⁠\[0, 1\]⁠ using normalized variable. The default is function function(v) { hsv(0,1,v) }.
Otherwise df[,clr] is converted to a factor and palcol must be a function which returns for each level a color. The parameter for palcol is the numbe of levels and the default is grDevices::rainbow(). If the length of clr is the number of rows of df then clr is interpreted as colors.

Andrews curves transform multidimensional data into curves. This package presents four types of curves.

Value

nothing

Author(s)

Sigbert Klinke [email protected], Jaroslav Myslivec [email protected]

References

Andrews, D. F. (1972) Plots of High-Dimensional Data. Biometrics, vol. 28, no. 1, pp. 125-136.
Khattree, R., Naik, D. N. (2002) Andrews Plots for Multivariate Data: Some New Suggestions and Applications. Journal of Statistical Planning and Inference, vol. 100, no. 2, pp. 411-425.

Examples

data(iris)
op <- par(mfrow=c(1,2))
andrews0(iris,clr=5,ymax=3)
andrews(iris,clr=5,ymax=3)
par(op)
andrews(iris,type=4,clr=5,ymax=NA)
data(iris)
op <- par(mfrow=c(1,2))
andrews0(iris,clr=5,ymax=3)
andrews(iris,clr=5,ymax=3)
par(op)
andrews(iris,type=4,clr=5,ymax=NA)

Andrews curves

Description

Andrews curves for visualization of multidimensional data. For differences between andrews and andrews2 see the 'vignette("andrews"). For colouring the curves see the details.

Usage

andrews0(
  df,
  type = 1,
  clr = NULL,
  step = 100,
  ymax = 10,
  main = NULL,
  sub = NULL
)
andrews0(
  df,
  type = 1,
  clr = NULL,
  step = 100,
  ymax = 10,
  main = NULL,
  sub = NULL
)

Arguments

`df`	data frame
`type`	type of curve `1`: $f(t)=x_1/\sqrt{2}+x_2\sin(t)+x_3\cos(t)+x_4\sin(2t)+x_5\cos(2t)+...$ `2`: $f(t)=x_1\sin(t)+x_2\cos(t)+x_3\sin(2t)+x_4\cos(2t)+...$ `3`: $f(t)=0.5^{p/2}x_1+0.5^{(p-1)/2} x_2(\sin(t)+\cos(t))+0.5^{(p-2)/2} x_3(\sin(t)-\cos(t))+0.5^{(p-3)/2} x_4(\sin(2t)+\cos(2t))+0.5^{(p-6)/2}x_5(\sin(2t)-\cos(2t))+...)$ with $p$ the number of variables `4`: $f(t)=1/\sqrt{2}(x_1+x_2(\sin(t)+\cos(t))+x_3(\sin(t)-\cos(t))+x_4(\sin(2t)+\cos(2t))+x_5(\sin(2t)-\cos(2t))+...)$
`clr`	number/name of column in the date frame for color of curves
`step`	smoothness of curves
`ymax`	maximum of `y` coordinate.
`main`	main title for the plot
`sub`	sub title for the plot

Details

Andrews curves transform multidimensional data into curves. This package presents four types of curves

If df[,clr] is numeric then hsv(1,1,v) with the normalized values (on ⁠\[0, 1\]⁠) of df[,clr] is used. Otherwise the number of unique values in nuv <- unique(df[,clr]) is used in connection with rainbow(nuv).

Value

nothing

Author(s)

Jaroslav Myslivec [email protected]

References

Andrews, D. F. (1972) Plots of High-Dimensional Data. Biometrics, vol. 28, no. 1, pp. 125-136.
Khattree, R., Naik, D. N. (2002) Andrews Plots for Multivariate Data: Some New Suggestions and Applications. Journal of Statistical Planning and Inference, vol. 100, no. 2, pp. 411-425.

Examples

data(iris)
andrews0(iris,clr=5,ymax=3)
andrews0(iris,type=4,clr=5,ymax=2)
data(iris)
andrews0(iris,clr=5,ymax=3)
andrews0(iris,type=4,clr=5,ymax=2)

Swiss banknotes data

Description

The data set contains six measurements made on 100 genuine and 100 counterfeit old-Swiss 1000-franc bank notes. The data frame and the documentation is a copy of mclust::banknote.

Usage

banknote
banknote

Format

A data frame with 200 rows and 7 columns:

Status: the status of the banknote: genuine or counterfeit
Length: Length of bill (mm)
Left: Width of left edge (mm)
Right: Width of right edge (mm)
Bottom: Bottom margin width (mm)
Top: Top margin width (mm)
Diagonal: Length of diagonal (mm)

Source

Flury, B. and Riedwyl, H. (1988). Multivariate Statistics: A practical approach. London: Chapman & Hall, Tables 1.1 and 1.2, pp. 5-8.

deftype

Description

Defines a function which can be used as basis for Andrews curves $f_t(t) = \sum_{j=1}^p x_{ij} f_i(t)$ .

Usage

deftype(index = NULL, FUN = NULL, xlim = c(-pi, pi))
deftype(index = NULL, FUN = NULL, xlim = c(-pi, pi))

Arguments

`index`	index/name of the function
`FUN`	function of the form `function(n, t) {...}`
`xlim`	default range for displaying curves (default: `c(-pi,pi)`)

Value

either a list of all functions or a single function

Examples

# define a new andrews curve, just with sine curves
deftype("sine", function(n, t) {
          n <- as.integer(if (n<1) 1 else n)
          m <- matrix(NA, nrow=length(t), ncol=n)
          for (i in 1:n) m[,i] <- sin(i*t)
          m
         })
andrews(iris, "sine")
# query
deftype()
deftype("sine")
# define a new andrews curve, just with sine curves
deftype("sine", function(n, t) {
          n <- as.integer(if (n<1) 1 else n)
          m <- matrix(NA, nrow=length(t), ncol=n)
          for (i in 1:n) m[,i] <- sin(i*t)
          m
         })
andrews(iris, "sine")
# query
deftype()
deftype("sine")

Generate a Sequence of Prime Numbers

Description

Generates a vector of the first n primes using gmp::nextprime().

Usage

generate_n_primes(n, one = FALSE)
generate_n_primes(n, one = FALSE)

Arguments

`n`	the number of primes to generate.
`one`	should `1` included in the sequence (default: `FALSE`)

Value

an integer vector of prime numbers

Examples

generate_n_primes(5)
generate_n_primes(5, TRUE)
generate_n_primes(5)
generate_n_primes(5, TRUE)

Normalization

Description

Normalization of a variable:

type==1: ar normalized into $[0,1]$ ,
type==2: ar is standardized,
otherwise no normalization is done.

Usage

normalize(ar, type = 1)
normalize(ar, type = 1)

Arguments

`ar`	numeric variable.
`type`	integer: type of normalization (default: `1`)

Details

Normalization of variable: ar<-(ar-min(ar))/(max(ar)-min(ar))

Value

Returns normalized variable.

Author(s)

Jaroslav Myslivec [email protected], Sigbert Klinke [email protected]

Examples

normalize(iris[,1])
normalize(iris[,1])

Numeric array

Description

Extracts numeric array from data frame.

Usage

numarray(df)
numarray(df)

Arguments

`df`	data frame.

Details

Extracts numeric array from data frame.

Value

Returns numeric array.

Author(s)

Jaroslav Myslivec [email protected], Sigbert Klinke [email protected]

Examples

numarray(iris)
numarray(iris)

outlyingness

Description

Computes the Stahel-Donoho outlyingness. If type is any of the available types by andrews() then the projection vectors are generated along the andrews curves. Otherwise step random directions will be used. Note that the projection vectors are always normalized to length one.

Usage

outlyingness(x, type = 1, step = 100, xlim = NULL, normalize = 1)
outlyingness(x, type = 1, step = 100, xlim = NULL, normalize = 1)

Arguments

`x`	data frame
`type`	type of curve, see `andrews()`
`step`	step smoothness of curves
`xlim`	the x limits (x1, x2)
`normalize`	type of normalization, see `normalize()`

Value

the Stahel-Donoho outlyingness

References

Stahel, W. (1981), Robuste Schätzungen: infinitesimale Optimalität und Schätzungen von Kovarianzmatrizen, PhD thesis, ETH Z¨urich.
Donoho, D. (1982), Breakdown properties of multivariate location estimators, Ph.D. Qualifying paper, Dept. Statistics, Harvard University, Boston.

Examples

# use projection vectors from the Andrews curve
sdo <- outlyingness(iris)
col <- gray(1-sdo/max(sdo))
andrews(iris, clr=col, ymax=NA)
# use 1000 random projection vectors
sdo <- outlyingness(iris, type=0, step=1000)
col <- gray(1-sdo/max(sdo))
andrews(iris, clr=col, ymax=NA)
# use 1000 random projection vectors with adjusted outlyingness
library("robustbase")
x   <- numarray(iris)
x   <- scale(x, center=apply(x, 2, min), scale=apply(x, 2, max)-apply(x, 2, min))
sdo <- adjOutlyingness(x, ndir=1000, only.outlyingness=TRUE)
col <- gray(1-sdo/max(sdo))
andrews(as.data.frame(x), clr=col, ymax=NA)
# use projection vectors from the Andrews curve
sdo <- outlyingness(iris)
col <- gray(1-sdo/max(sdo))
andrews(iris, clr=col, ymax=NA)
# use 1000 random projection vectors
sdo <- outlyingness(iris, type=0, step=1000)
col <- gray(1-sdo/max(sdo))
andrews(iris, clr=col, ymax=NA)
# use 1000 random projection vectors with adjusted outlyingness
library("robustbase")
x   <- numarray(iris)
x   <- scale(x, center=apply(x, 2, min), scale=apply(x, 2, max)-apply(x, 2, min))
sdo <- adjOutlyingness(x, ndir=1000, only.outlyingness=TRUE)
col <- gray(1-sdo/max(sdo))
andrews(as.data.frame(x), clr=col, ymax=NA)

Selecting in Andrews curves

Description

Selecting object utility in Andrews curves

Usage

selectand(df, type = 1, step = 100, ncol = 0, from = 0, to = 1, col = 2)
selectand(df, type = 1, step = 100, ncol = 0, from = 0, to = 1, col = 2)

Arguments

`df`	data frame.
`type`	type of curve.
`step`	smoothness of curves.
`ncol`	number of column in data frame for selection.
`from`	from value.
`to`	to value.
`col`	color of selected objects.

Details

Define which objects will be selected (colored) in Andrews curves.

Value

Nothing

Author(s)

Jaroslav Myslivec [email protected]

Examples

data(iris)
andrews(iris,clr=5,ymax=3)
selectand(iris,ncol=1,from=5,to=5.5,col=1)
data(iris)
andrews(iris,clr=5,ymax=3)
selectand(iris,ncol=1,from=5,to=5.5,col=1)

Comparison

Description

Creates and displays a temporary PDF file with different diagrams comparing andrews and andrews0 plots.

Usage

zzz()
zzz()

Value

nothing

Examples

if (interactive()) zzz()
if (interactive()) zzz()

Package 'andrews'

Help Index

Andrews curves

Description

Usage

Arguments

Details

Value

Author(s)

References

Examples

Andrews curves

Description

Usage

Arguments

Details

Value

Author(s)

References

Examples

Swiss banknotes data

Description

Usage

Format

Source

deftype

Description

Usage

Arguments

Value

Examples

Generate a Sequence of Prime Numbers

Description

Usage

Arguments

Value

Examples

Normalization

Description

Usage

Arguments

Details

Value

Author(s)

Examples

Numeric array

Description

Usage

Arguments

Details

Value

Author(s)

Examples

outlyingness

Description

Usage

Arguments

Value

References

Examples

Selecting in Andrews curves

Description

Usage

Arguments

Details

Value

Author(s)

Examples

Comparison

Description

Usage

Value

Examples